Born in Glengormley, County Antrim, Northern Ireland and brought up in Boardmills, County Down, Blackshaw attended Methodist College Belfast and studied at Belfast College of Art (1948–1951). In 1951 Blackshaw was awarded a scholarship by the Committee for the Encouragement of Music and the Arts, to study in Paris.

He was initially acclaimed for his mastery of traditional approaches to painting. He continued to develop as an artist becoming most highly regarded for his very loose gestural application of paint and a very distinctive and subtle use of colour. His paintings of such sports as horse racing and boxing have made him particularly popular but Blackshaw is also a talented portrait painter.

Blackshaw's painting are very often figurative in form, but with a non-naturalistic palate which rebalances the composition in an expressionist, even abstract, way. His themes are very Irish and often rural; greyhounds, Irish Travellers and the landscape. He has also produced portraits and has designed posters for Derry's Field Day Theatre Company.